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rudyjanay Group Title

A grain silo is shown below. What is the volume of grain that could completely fill this silo rounded to the nearest whole number? Use 22/7 for pi. 19,008 ft3 19,461 ft3 6,336 ft3 453 ft3

  • 2 years ago
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  1. rudyjanay Group Title
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    • 2 years ago
  2. agentx5 Group Title
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    Sum together half of a sphere for the top part, with a cylinder for the bottom part. That's all there is to it :-) Do you know the formulas for a cylinder and a sphere? h = 168 ft r = 6 ft

    • 2 years ago
  3. rudyjanay Group Title
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    no i don't

    • 2 years ago
  4. agentx5 Group Title
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    \[\large V_{sphere} = \frac{4 \pi r ^3}{3}\] \[\large V_{cylinder} = \pi r^2 h\] \[V_{total} = \frac{V_{sphere}}{2} + V_{cylinder}\]

    • 2 years ago
  5. agentx5 Group Title
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    Can you solve it now? ;-D

    • 2 years ago
  6. rudyjanay Group Title
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    no i'm sorry i'm completely lost :-(

    • 2 years ago
  7. agentx5 Group Title
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    r = radius (both for the cylinder and sphere) , h = height of the cylinder Separate the curved, hemispherical top from the cylinder under it. You'll just add volume the two shapes together. What are you confused on specifically?

    • 2 years ago
  8. rudyjanay Group Title
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    i'm just naturally confused on everything that has to do with maths you have to talk to me like a toddler and tell mi step by step

    • 2 years ago
  9. agentx5 Group Title
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    Can you identify the radius in the drawing? And the height?

    • 2 years ago
  10. rudyjanay Group Title
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    the radius for the entire drawing?

    • 2 years ago
  11. agentx5 Group Title
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    There's only one radius, yes. It works for both the sphere and cylinder, like I said.

    • 2 years ago
  12. rudyjanay Group Title
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    is it 6 ft?

    • 2 years ago
  13. agentx5 Group Title
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    Yes... |dw:1342123496209:dw|

    • 2 years ago
  14. agentx5 Group Title
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    And height is "h", which is?

    • 2 years ago
  15. rudyjanay Group Title
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    168 ft

    • 2 years ago
  16. abhishekjha29 Group Title
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    2/3*22/7*6*6*6 + 1/3*@22/7*6*6*168 = ............

    • 2 years ago
  17. agentx5 Group Title
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    Ok, now scroll up and put r & h into those two equations for the Volume of a Sphere and Cylinder. Substitute, replacing r with "(6 ft)", and replacing h with "(168 ft)".

    • 2 years ago
  18. rudyjanay Group Title
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    ok

    • 2 years ago
  19. abhishekjha29 Group Title
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    |dw:1342123834485:dw| find the volume of given figure

    • 2 years ago
  20. agentx5 Group Title
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    @abhishekjha29 no, it's a cylinder under a hemisphere, not a cone.

    • 2 years ago
  21. abhishekjha29 Group Title
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    ya tats ok.but i have a new figure wid a cone instead of culinder

    • 2 years ago
  22. rudyjanay Group Title
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    so i use 3/4 3.14 times 6 to the 3rd power to find the volume of the sphere?

    • 2 years ago
  23. agentx5 Group Title
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    ??? @abhishekjha29 the volume of a cone = \(\large\frac{\pi r ^2 h}{3}\) , exactly a third of a cylinder's volume with the same dimensions for height and radius.

    • 2 years ago
  24. rudyjanay Group Title
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    oh ok

    • 2 years ago
  25. rudyjanay Group Title
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    when i do it it tells me that the volume for the cylinder is 6330.24

    • 2 years ago
  26. agentx5 Group Title
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    @rudyjanay I would leave the 3.1415... \(\pi\) out of it until the end, just keep it along like it's a unit like "feet". You can indeed do that above, but keep in mind it will be an estimate because: \(\pi \approx 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 062...\)

    • 2 years ago
  27. agentx5 Group Title
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    Best to just leave it alone until you're all done with the formulas :-D

    • 2 years ago
  28. agentx5 Group Title
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    Kind of like how I did in the cylinder part above, if you see what I did

    • 2 years ago
  29. agentx5 Group Title
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    When you're all done, multiply that big, non-decimal number and it'll give you your messy decimal answer.

    • 2 years ago
  30. rudyjanay Group Title
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    ok i'll try leaving the 3.14 out

    • 2 years ago
  31. agentx5 Group Title
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    :-) I think you've got it down now It's just plug & chug once you got the setup up done. The tricky part was recognizing it's half of a sphere (a hemisphere) plus a cylinder added together, and that the cylinder and the hemisphere have the same radius.

    • 2 years ago
  32. rudyjanay Group Title
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    oh i guess my phone was giving me the wrong answer because i don't have a calculator with me

    • 2 years ago
  33. rudyjanay Group Title
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    the answer that i got is 19 461

    • 2 years ago
  34. agentx5 Group Title
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    I just noticed I made a typo let me correct myself... \[\large V_{cylinder} = \pi r^2 h\] \[\large V_{cylinder} = \pi (6 \ ft)^2 (168 \ ft)\] \[\large V_{cylinder} = \pi (36 \ ft^2)(168 \ ft)\] \[\large V_{cylinder} = 6048\pi \ ft^3\] And back into the total... \[\large V_{total} = \frac{288\pi \ ft^3}{2} + (6048\pi ft^3)\] \[\large V_{total} = 144\pi \ ft^3 + 6048\pi ft^3\] \[\large V_{total} = 6192\pi \ ft^3 \approx \ 19452.74171... ft^3\]

    • 2 years ago
  35. rudyjanay Group Title
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    oh so i was right

    • 2 years ago
  36. agentx5 Group Title
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    So yes, you're good. The answer choice you were given is actually an estimate, and not as exact as what I just did :-)

    • 2 years ago
  37. rudyjanay Group Title
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    ohhhh great thank you

    • 2 years ago
  38. agentx5 Group Title
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    6292\(\pi\) ft\(^3\) is the exact answer, and what I would be expect to do at work

    • 2 years ago
  39. agentx5 Group Title
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    Because if a construction firm wants to make an estimate to their liking, they can just pull out their pocket calculator or smartphone and see how many decimal places they care about for the project

    • 2 years ago
  40. agentx5 Group Title
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    Sometimes accuracy is critical and a matter of life & death, other times you don't have to be so particular

    • 2 years ago
  41. rudyjanay Group Title
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    thats why i don't get maths

    • 2 years ago
  42. agentx5 Group Title
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    Example of where accuracy is a matter of life & death: ammunition factory. Even the smallest screw up could mean a detonation, a dud bullet in a critical field operation that means some cop or soldier gets killed, contracts being canceled etc. Another good example would be a factory where they make care engines. If they get the radius slightly wrong your engine won't work well or is more prone to breakdowns. Math can seem useless until you have something that makes it mean something :-)

    • 2 years ago
  43. agentx5 Group Title
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    Car engines* lol not "care"

    • 2 years ago
  44. rudyjanay Group Title
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    are you a math wiz or something

    • 2 years ago
  45. agentx5 Group Title
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    Engineering student. I'm not mathematician, but I love the application of it to stuff that matters :-3 Fire & explosives for example is a specialty of mine, and game design is my hobby (which also uses math quiet a bit because of physics stuff).

    • 2 years ago
  46. agentx5 Group Title
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    Math itself though, meh... I loose focus if it doesn't mean anything practical.

    • 2 years ago
  47. rudyjanay Group Title
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    oh ok i'm gonna check on my other question

    • 2 years ago
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